Finite Math Examples

$x + 4 y > 8$ , $x - 2 y < 8$

Step 1

Solve $x + 4 y > 8$ for $y$ .

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Step 1.1

Subtract $x$ from both sides of the inequality.

$4 y > 8 - x$

Step 1.2

Divide each term in $4 y > 8 - x$ by $4$ and simplify.

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Step 1.2.1

Divide each term in $4 y > 8 - x$ by $4$ .

$\frac{4 y}{4} > \frac{8}{4} + \frac{- x}{4}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} > \frac{8}{4} + \frac{- x}{4}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y > \frac{8}{4} + \frac{- x}{4}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $8$ by $4$ .

$y > 2 + \frac{- x}{4}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y > 2 - \frac{x}{4}$

Step 2

Solve $x - 2 y < 8$ for $y$ .

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Step 2.1

Subtract $x$ from both sides of the inequality.

$- 2 y < 8 - x$

Step 2.2

Divide each term in $- 2 y < 8 - x$ by $- 2$ and simplify.

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Step 2.2.1

Divide each term in $- 2 y < 8 - x$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} > \frac{8}{- 2} + \frac{- x}{- 2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} > \frac{8}{- 2} + \frac{- x}{- 2}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y > \frac{8}{- 2} + \frac{- x}{- 2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Divide $8$ by $- 2$ .

$y > - 4 + \frac{- x}{- 2}$

Step 2.2.3.1.2

Dividing two negative values results in a positive value.

$y > - 4 + \frac{x}{2}$

Step 3

Find the intersection of $y > 2 - \frac{x}{4}$ and $y > - 4 + \frac{x}{2}$ .

$y > 2 - \frac{x}{4}$ and $y > - 4 + \frac{x}{2}$

Step 4